1. Field of the Invention
The invention relates generally to the field of seismic data processing methods. More specifically, the invention relates for methods for estimating seismic compressional wave anisotropy for use in pre-stack migration imaging.
2. Background Art
Seismic surveying is used to evaluate structures of, compositions of, and fluid content of subsurface earth formations. A particular application for seismic surveying is to infer the presence of useful materials, such as petroleum, in the subsurface earth formations. Generally, seismic surveying includes deploying an array of seismic sensors at or near the earth's surface, and deploying a seismic energy source near the sensors also at or near the surface. The seismic energy source is actuated and seismic energy emanates from the source, traveling generally downwardly through the subsurface until it reaches one or more acoustic impedance boundaries. Seismic energy is reflected from the one or more impedance boundaries, where it then travels upwardly until being detected by one or more of the sensors. Structure and composition of the subsurface is inferred from the travel time of the seismic energy, and the amplitude and phase of the various frequency components of the seismic energy with respect to the energy emanating from the seismic source.
In order to infer the structures of subsurface earth formations from seismic travel times measured at the earth's surface from a source position at the surface, it is necessary to determine the velocity of the various formations through which the seismic energy passes. Velocities of the earth formations can vary both with respect to depth in the earth (vertically), and with respect to geographic position (laterally). Seismic data, however, are recorded only with respect to time. Methods known in the art for estimating velocities of the earth formations .both vertically and laterally rely on inferences about the travel path geometry of the seismic energy as it travels from the seismic source to the various seismic receivers deployed at the earth's surface.
Migration is a process performed on seismic data in which depth estimates to one or more reflective horizons (acoustic impedance boundaries) in the earth are made from the “two way” travel time of seismic energy from the source, to the reflective horizons, and back to the seismic receivers. The depth estimates are computed and displayed with respect to geographic position of the reflective horizons. Depth estimates based on two way travel time must be corrected for the effects of seismic energy travel path differences between various seismic energy source and receiver geographic positions that are used during data acquisition. In order to correct the depth estimates for source and receiver positions, it is necessary to accurately estimate the velocity of seismic energy in the earth from the earth's surface to (or the ocean bottom in marine seismic data) to each subsurface reflective horizon. Methods are known in the art for estimating velocity from two way travel time from the seismic source to the reflective horizons and back to the seismic receivers.
It is known in the art that some earth formations are anisotropic with respect to seismic velocity. Anisotropy can be observed as different velocity in a single medium depending on the direction of propagation of the seismic energy through the medium. In anisotropic earth formations, the depth estimating (imaging) process needs to take the anisotropy into account in order to accurately position the seismic reflective horizons with respect to depth and geographic position. Reliable estimation of anisotropy parameters is thus important to accurate depth imaging. Because the anisotropy parameters and velocity are related, however, estimation of anisotropy parameters is not trivial and is often unstable using methods known in the art.
It is known in the art to estimate certain anisotropy parameters (called “anelliptic” parameters) from prestack seismic data. “Prestack” seismic data are seismic data traces (traces being a term used in the art for a record of the signal detected by one of the seismic receivers) that have not been summed, average, or otherwise processed together with any other seismic data trace. See for example, Alkhalifah, T., Velocity analysis using nonhyperbolic moveout in transversely isotropic media, Geophysics 62, 1839–1845 (1997). See also Lou, M., Pham, L. D. and Lee, S., Anisotropic parameter estimation from joint P- and C-wave data, 64th Ann. Mtg., Eur. Assn. Geosci. Eng., Florence (2002). See also, Martinez, R. D. and Lee, S., 2002, A strategy for anisotropic P-wave prestack imaging, 72nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 149–152 (2002).
A method disclosed in the Martinez and Lee reference, for example, combines prestack time migrations and prestack depth migrations for estimating the anisotropic parameters and velocities. The method disclosed in the Martinez and Lee reference has been shown to generate an accurate result for the effective anelliptical (ηeff) parameter. FIG. 1 shows a flow chart of the method disclosed in the Martinez and Lee reference. At 10, seismic data can be prestack time migrated. At 11, the prestack time migrated data may be scanned to obtain a model of NMO velocity and effective anelliptical parameters. The effective parameter model may be processed, at 12, to obtain interval velocity and anelliptical parameter models. Sonic logs, check shot surveys, and/or vertical seismic profile (VSP) data, at 13, may be used to derive the vertical velocity model. Alternatively, at 16, the interval parameter model may be put through an anisotropic ray tracing procedure, and at 15, the data are prestack depth migrated. The interval velocity and anelliptical parameter model may be adjusted in depth, at 14, and the ray tracing and depth migration are repeated until a satisfactory result is obtained.
The effective parameters ηeff and Vnmo with respect to two-way seismic travel time, obtained from the prestack time migration, need to be converted into “interval” parameters ηint and Vint with respect to depth, as explained in the Martinez and Lee reference. ηint is described in the Martinez and Lee reference as being inverted from the effective anelliptical parameter (ηeff). The effective anelliptical parameter is equivalent to an average anelliptical parameter from the earth's surface or water bottom to a selected depth in the subsurface) and effective velocity (Vnmo). Both the effective velocity and effective anelliptical parameter are typically determined by “scanning” compressional (P-wave) moveout on common-image gathers from prestack time migration. Scanning refers to the process of calculating a correlation or semblance between selected seismic traces after adjusting using various values of compressional velocity and effective anelliptical parameter. Because the selected traces typically represent different source to receiver distances (offsets), the semblance between traces will be related to the moveout velocity and anelliptical parameter of the earth formations between the seismic source and the one of the seismic receivers used to record each trace. The values of compressional velocity and anelliptical parameter which provide the greatest value of semblance are selected as the effective (or normal moveout) velocity and anelliptical parameters. The values of effective anelliptical parameter and normal moveout velocity are then used to obtain values of interval velocity and interval anelliptical parameter. The inversion to obtain each set of interval values is performed using the well known Dix equation. The parameters determined using the Dix equation are then used to generate a prestack depth migrated image. The image is checked for error, and the values of interval parameters are adjusted, and the prestack depth migrated image is generated again, as explained above with respect to FIG. 1. The foregoing procedure is repeated until the image error is determined to be at a minimum, or below a selected threshold. Image error is determined by lack of “flatness” (consistency in two way time to a particular reflective horizon) in common image gathers (CIGs).
Because of its differential nature, however, the Dix equation boosts errors present in the inputs (the effective velocities and effective anelliptical parameters), making its output unstable. This is especially true in the inversion for the anelliptical parameter ηint because the velocity is related to the anelliptical parameter by the 4th power of the velocity. Thus, relatively small errors in the velocity can be translated into much larger errors in the output interval anelliptical parameters ηint. There thus exists a need for a better technique to determine interval anelliptical parameters from seismic data.